# Formula Chart for Numbers and Operations on the SBAC Test

Most people say that Math is hard for them. Does this sound like you? Are you wondering how to ace the SBAC Test? Well,

Math is like music: a set of rules that, when applied correctly, create beauty.

Do you want to succeed on the SBAC Test? You’ll need to know the rules. In the following chart, you’ll find the essential rules you’ll need to apply when solving Numbers and Operations Questions on the SBAC Test. Use the rules and create your own “math music.”

Also, be sure and utilize our four other formula charts as you prepare for this test:

Algebra

Functions

Geometry

Statistics and Probability

## Numbers and Operations Formulas for the SBAC

Category Formula Symbols Comment
Properties of
Rational
Numbers
$$a+b=b+a$$

$$a \cdot b = b \cdot a$$
a, b = any constant or variable Commutative
Property
Properties of
Rational
Numbers
$$a+(b+c)=(a+b)+c$$

$$a \cdot (b \cdot c)=(a \cdot b) \cdot c$$
a, b, c = any constant or variable Associative
Property
Properties of
Rational
Numbers
$$a \cdot (b+c)=a \cdot b + a \cdot c$$ a, b, c = any constant or variable Distributive
Property
Properties of
Rational
Numbers
$$a+0=a$$ a = any constant or variable Identity Property
Properties of
Rational
Numbers
$$a \cdot 1 = a$$ a = any constant or variable Identity Property
of Multiplication
Properties of
Rational
Numbers
$$\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \cdot d)+(c \cdot b)}{(b \cdot d)}$$ a, b, c, d = any real number Remember to simplify
the fraction if
possible.
Properties of
Rational
Numbers
$$\dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c)}{(b \cdot d)}$$ a, b, c, d = any real number Remember to simplify
the fraction if
possible.
Properties of
Rational
Numbers
$$\dfrac{a}{b} \div \dfrac{c}{d}=\dfrac{a \cdot d)}{(b \cdot c)}$$ a, b, c, d = any real number Remember to simplify
the fraction if
possible.
Properties of
Rational
Numbers
$$a\dfrac{b}{c}=\dfrac{(a \cdot c)+b}{c}$$ a, b, c = any real number Remember to simplify
the fraction if
possible.
Properties of
Exponents
$$x^a \cdot x^b = x^{a+b}$$
a, b, x = any real number
Remember to simplify
the fraction if
possible.
Properties of
Exponents
$$\frac{x^a}{x^b}=x^{a-b}$$
a, b, x = any real number

Properties of
Exponents
$$(x^a)^b = x^{a \cdot b}$$
a, b, x = any real number

Properties of
Exponents
$$(x \cdot y)^a = x^a \cdot y^a$$
a, x, y = any real number

Properties of
Exponents
$$x^1 = x$$
x = any real number

Properties of
Exponents
$$P=(2 \cdot l)+(2 \cdot w)$$ x = any real number

Properties of
Exponents
$$x^{-a} = \frac {1}{x^a}$$
a, x = any real number

Percentages $$a \cdot b\%=a \cdot \dfrac{b}{100}$$
a = any real number
b% = any percent
Remember to simplify
if possible.
Percentages $$\% = \dfrac{\vert b-a \vert}{b} \cdot 100= \dfrac{c}{b} \cdot 100$$
% = % increase or decrease
a = new value
b = original value
c = amount of change

Units $$Du=Su \cdot \dfrac{Du}{Su}=Su \cdot CF$$
Du = Desired Unit
Su = Starting Unit
CF = Conversion Factor
Multiple steps may
be needed